Exercise 1.1 - Chapter 1 Number Systems Term 1 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question $2 .$
Say True or False.
(i) The additive inverse of $(-32)$ is $-32$
(ii) $(-90)+(-30)=60$
(iii) $(-125)+25=-100$

Solution:
(i) False
(ii) False
(iii) True

Question $3 .$
Add the following.
(i) 8 and-12 using number line.
Solution:
Starting at zero on the number line facing positive direction and move 8 steps forward reaching 8 .

Then we move 12 steps
backward to represent $-12-$
and reach at $-4$.
$\therefore 8+(-12)=-4$
(ii) $(-3)$ and $(-5)$ using number line.
Solution:
Starting at zero on the number line facing positive direction and move 3 steps backward reaching- $3 .$

Then we move 5 steps backward to represent $-5$ and reach $-8$. $\therefore(-3)+(-5)=-8$
(iii) $(-100)+(-10)$
Solution:
$(-100)+(-10)=-100-10=-110$
(iv) $20+(-72)$
Solution: $20+(-72)=20-72=-52$
$20+(-72)=20-72=-52$
(v) $82+(-75)$
Solution:
$82+(-75)=82-75=7$
(vi) $-48+(-15)$
Solution:
$-48+(-15)=-48-15=-63$

(vii) $-225+(-63)$
Solution:
$-225+(-63)=-225-63=-288$

Question $4 .$
Thenmalar appeared for competitive exam which has negative scoring of 1 mark for each incorrect answers. In paper I she answered 25 question incorrectly and in paper II13 questions incorrectly. Find the total reduction of marks.
Solution:
For each incorrect question the score $=-1$
In paper I, score for 25 incorrect questions $-25 \times(-1)=-25$
In paper II, for 13 incorrect question the score $=13 \times(-1)=-13$
The total marks get reduced $=(-25)+(-13)=-38$
$-38$ marks will be reduced.

Question $5 .$
In a quiz competition, Team A scored $+30,-20,0$ and team B scored $-20,0,+30$ in three successive rounds. Which team will win? Can we say that we can add integers in any order?
Solution:
Total score of team $A=[(+30)+(-20)]+0=(+10)+0=10$
Total score of team B $=[(-20)+0]+(+30)$
$=-20+30=+10$
Score of team $\mathrm{A}=$ Score of team $\mathrm{B}$.
Yes, we say that we can add integers in any order.

Question $6 .$
Are $(11+7)+10$ and $11+(7+10)$ equal? Mention the property.
Solution:
First we take $(11+7)+10=18+10=28$
Now $11+(7+10)=11+17=28$
In both the cases the sum is $28 . \therefore(11+7)+10=11+(7+10)$
This property is known as associative property of integers under addition.

Question $7 .$
Find 5 pairs of integers that added to 2 .
Solution:
$\begin{aligned}
&0+2=2 \\
&1+1=2 \\
&-1+3=2 \\
&-2+4=2 \\
&-3+5=2 \text { (and many more.) }
\end{aligned}$

Question $8 .$
The temperature at 12 noon at a certain place was $18^{\circ}$ above zero. If it decreases at the rate of $3^{\circ}$ per hour at what time if would be $12^{\circ}$ below zero?
(i) 12 mid night
(ii) 12 noon
(iii) $10 \mathrm{am}$
(iv) $10 \mathrm{pm}$
Solution:
(iv) $10 \mathrm{pm}$
: 'Temperature at 12 noon $=18^{\circ}$ above zero $=+18^{\circ}$
Rate of decrease per hour $=-3^{\circ}$
Temperature $12^{\circ}$ below zero $=-12^{\circ}$
$-12$ is 30 units to the left of $+18^{\circ}$
Time at which it reach $-12^{\circ}=\frac{30}{3}=10 \mathrm{~h}$
$10 \mathrm{hrs}$ after 12 noon $=10 \mathrm{pm}$

Question $9 .$
Identify the problem with negative numbers as its answer.
(i) $-9+(-5)+6$
(ii) $8+(-12)-6$
(iii) $-4+2+10$
(iv) $10+(-4)+8$
Solution:
(i) $-9+(-5)+6$
(i) $-9+(-5)+6=-14+6=-8$
(ii) $8+(-12)+6=-4+6=-2$
(iii) $-4+2+10=-2+10=8$
(iv) $10+(-4)+8=6+8=14$

Question $10 .$
$(-10)+(+7)=$
(i) $+3$
(ii) $-3$
(iii) $-17$
(iv) $+17$
Solution:
(ii) $-3$

Question $11 .$
$(-8)+10+(-2)=$
(i) 2
(ii) 8
(iii) 0
(iv) 20
Solution:
(iii) 0

Question $12 .$
$20+(-9)+9=$
(i) 20
(ii) 29
(iii) 11
(iv) 38
Solution:
(i) 20